The following study explores various characteristics of red wine including pH, citric acid, and residual sugars to determine which factors could be used to predict quality. These characteristics are compared to the ratings of three wine experts. The relationships between these variables are explored throughout this study.
## [1] 1599 13## 'data.frame': 1599 obs. of 13 variables:
## $ X : int 1 2 3 4 5 6 7 8 9 10 ...
## $ fixed.acidity : num 7.4 7.8 7.8 11.2 7.4 7.4 7.9 7.3 7.8 7.5 ...
## $ volatile.acidity : num 0.7 0.88 0.76 0.28 0.7 0.66 0.6 0.65 0.58 0.5 ...
## $ citric.acid : num 0 0 0.04 0.56 0 0 0.06 0 0.02 0.36 ...
## $ residual.sugar : num 1.9 2.6 2.3 1.9 1.9 1.8 1.6 1.2 2 6.1 ...
## $ chlorides : num 0.076 0.098 0.092 0.075 0.076 0.075 0.069 0.065 0.073 0.071 ...
## $ free.sulfur.dioxide : num 11 25 15 17 11 13 15 15 9 17 ...
## $ total.sulfur.dioxide: num 34 67 54 60 34 40 59 21 18 102 ...
## $ density : num 0.998 0.997 0.997 0.998 0.998 ...
## $ pH : num 3.51 3.2 3.26 3.16 3.51 3.51 3.3 3.39 3.36 3.35 ...
## $ sulphates : num 0.56 0.68 0.65 0.58 0.56 0.56 0.46 0.47 0.57 0.8 ...
## $ alcohol : num 9.4 9.8 9.8 9.8 9.4 9.4 9.4 10 9.5 10.5 ...
## $ quality : int 5 5 5 6 5 5 5 7 7 5 ...## X fixed.acidity volatile.acidity citric.acid
## Min. : 1.0 Min. : 4.60 Min. :0.1200 Min. :0.000
## 1st Qu.: 400.5 1st Qu.: 7.10 1st Qu.:0.3900 1st Qu.:0.090
## Median : 800.0 Median : 7.90 Median :0.5200 Median :0.260
## Mean : 800.0 Mean : 8.32 Mean :0.5278 Mean :0.271
## 3rd Qu.:1199.5 3rd Qu.: 9.20 3rd Qu.:0.6400 3rd Qu.:0.420
## Max. :1599.0 Max. :15.90 Max. :1.5800 Max. :1.000
## residual.sugar chlorides free.sulfur.dioxide
## Min. : 0.900 Min. :0.01200 Min. : 1.00
## 1st Qu.: 1.900 1st Qu.:0.07000 1st Qu.: 7.00
## Median : 2.200 Median :0.07900 Median :14.00
## Mean : 2.539 Mean :0.08747 Mean :15.87
## 3rd Qu.: 2.600 3rd Qu.:0.09000 3rd Qu.:21.00
## Max. :15.500 Max. :0.61100 Max. :72.00
## total.sulfur.dioxide density pH sulphates
## Min. : 6.00 Min. :0.9901 Min. :2.740 Min. :0.3300
## 1st Qu.: 22.00 1st Qu.:0.9956 1st Qu.:3.210 1st Qu.:0.5500
## Median : 38.00 Median :0.9968 Median :3.310 Median :0.6200
## Mean : 46.47 Mean :0.9967 Mean :3.311 Mean :0.6581
## 3rd Qu.: 62.00 3rd Qu.:0.9978 3rd Qu.:3.400 3rd Qu.:0.7300
## Max. :289.00 Max. :1.0037 Max. :4.010 Max. :2.0000
## alcohol quality
## Min. : 8.40 Min. :3.000
## 1st Qu.: 9.50 1st Qu.:5.000
## Median :10.20 Median :6.000
## Mean :10.42 Mean :5.636
## 3rd Qu.:11.10 3rd Qu.:6.000
## Max. :14.90 Max. :8.000This dataset consists of 13 variables with 1599 observations.
## 75%
## 12.35## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 4.60 7.10 7.90 8.32 9.20 15.90Most wine have a fixed acidity between 6 and 11. There is a slight skew to the right with most wines having a fixed acidity of 11 or lower. There are multiple outliers in this distribution where the wines have fixed acidities higher than 12.35.
## 75%
## 1.015## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.1200 0.3900 0.5200 0.5278 0.6400 1.5800The wine with the lowest volatile acidity has a score of 0.12 and the highest has 1.58. Above, I plot the main body of volatile acidity, trimming those with the highest levels. There appears to be a bi modal distribution. There are multiple outliers in this distribution where the wines have volatile acidities higher than 1.015.
## 75%
## 0.915## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 0.090 0.260 0.271 0.420 1.000##
## 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14
## 132 33 50 30 29 20 24 22 33 30 35 15 27 18 21
## 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29
## 19 9 16 22 21 25 33 27 25 51 27 38 20 19 21
## 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43 0.44
## 30 30 32 25 24 13 20 19 14 28 29 16 29 15 23
## 0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59
## 22 19 18 23 68 20 13 17 14 13 12 8 9 9 8
## 0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74
## 9 2 1 10 9 7 14 2 11 4 2 1 1 3 4
## 0.75 0.76 0.78 0.79 1
## 1 3 1 1 1I transformed the long tail data to better understand the distribution of citric acidity. The wine with the lowest citric acid has a score of 0 while the highest has a score of 1. Most values lie between 0.09 and 0.42. The wine with the citric acid level of 1 is the only outlier in this distribution.
## 75%
## 3.65## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.900 1.900 2.200 2.539 2.600 15.500Most wines have a residual sugar level value between 1.9 and 2.6. I plotted those values that lie in this range and they appear to be normally distributed. The wine with the lowest residual sugar has a value of 0.9 and the highest has a score of 15.5. There are multiple outliers in this distribution where the wines have residual sugar levels higher than 3.65.
## 75%
## 0.12## 25%
## 0.04## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.01200 0.07000 0.07900 0.08747 0.09000 0.61100The chloride levels for the wines in the dataset range from 0.012 to 0.611. Most values lie between 0.07 and 0.09. I plotted the chloride levels for wines that had values within this range. These values appear to have a normal distribution. There are multiple outliers in this distribution where the wines have chloride levels higher than 0.12. There are also a handful of wines in the lower end of the distribution that are outliers with chloride levels less than 0.04.
## 75%
## 42## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.00 7.00 14.00 15.87 21.00 72.00## free.sulfur.dioxide
## 1 2 3 4 5 5.5 6 7 8 9 10 11 12 13 14
## 3 1 49 41 104 1 138 71 56 62 79 59 75 57 50
## 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
## 78 61 60 46 39 30 41 22 32 34 24 32 29 23 23
## 30 31 32 33 34 35 36 37 37.5 38 39 40 40.5 41 42
## 16 20 22 11 18 15 11 3 2 9 5 6 1 7 3
## 43 45 46 47 48 50 51 52 53 54 55 57 66 68 72
## 3 3 1 1 4 2 4 3 1 1 2 1 1 2 1Transforming the plot of free sulfur dioxide reveals a bi modal distribution. Most wines have values between 7 and 21. The lowest value is 1 and the highest is 72. There are multiple outliers in this distribution where the wines have free sulfur dioxide levels higher than 42.
## 75%
## 122## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 6.00 22.00 38.00 46.47 62.00 289.00## total.sulfur.dioxide
## 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
## 3 4 14 14 27 26 29 28 33 35 26 27 35 29 33
## 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
## 25 25 34 36 27 24 30 43 20 14 32 20 17 20 26
## 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
## 12 26 31 16 17 14 26 18 23 20 17 24 21 21 11
## 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
## 11 15 14 20 13 10 6 14 9 18 9 9 13 10 17
## 66 67 68 69 70 71 72 73 74 75 76 77 77.5 78 79
## 9 12 10 8 8 7 10 7 8 5 3 8 2 4 5
## 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94
## 4 6 4 2 6 9 10 6 14 9 5 7 8 2 8
## 95 96 98 99 100 101 102 103 104 105 106 108 109 110 111
## 4 5 7 6 3 4 6 2 5 5 6 3 4 6 3
## 112 113 114 115 116 119 120 121 122 124 125 126 127 128 129
## 3 4 2 2 1 7 2 4 3 3 2 1 2 2 3
## 130 131 133 134 135 136 139 140 141 142 143 144 145 147 148
## 1 3 3 2 2 2 1 1 3 1 2 3 3 3 2
## 149 151 152 153 155 160 165 278 289
## 1 2 1 1 1 1 1 1 1Total sulfur dioxide levels range between 6 and 289. Most values lie between 22 and 62. The maximum value is 289 and the minimum is 6. There are multiple outliers in this distribution where the wines have total sulfur dioxide levels higher than 122.
## 75%
## 1.001187## 25%
## 0.9922475
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.9901 0.9956 0.9968 0.9967 0.9978 1.0040The density of the wine’s in the dataset range from 0.9901 to 1.004. Most wines lie between 0.9956 and 0.9978. There are multiple outliers in this distribution where the wines have densities that are either higher than 1.001187 or lower than 0.9922475.
## 75%
## 3.685## 25%
## 2.925## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.740 3.210 3.310 3.311 3.400 4.010## pH
## 2.74 2.86 2.87 2.88 2.89 2.9 2.92 2.93 2.94 2.95 2.98 2.99 3 3.01 3.02
## 1 1 1 2 4 1 4 3 4 1 5 2 6 5 8
## 3.03 3.04 3.05 3.06 3.07 3.08 3.09 3.1 3.11 3.12 3.13 3.14 3.15 3.16 3.17
## 6 10 8 10 11 11 11 19 9 20 13 21 34 36 27
## 3.18 3.19 3.2 3.21 3.22 3.23 3.24 3.25 3.26 3.27 3.28 3.29 3.3 3.31 3.32
## 30 25 39 36 39 32 29 26 53 35 42 46 57 39 45
## 3.33 3.34 3.35 3.36 3.37 3.38 3.39 3.4 3.41 3.42 3.43 3.44 3.45 3.46 3.47
## 37 43 39 56 37 48 48 37 34 33 17 29 20 22 21
## 3.48 3.49 3.5 3.51 3.52 3.53 3.54 3.55 3.56 3.57 3.58 3.59 3.6 3.61 3.62
## 19 10 14 15 18 17 16 8 11 10 10 8 7 8 4
## 3.63 3.66 3.67 3.68 3.69 3.7 3.71 3.72 3.74 3.75 3.78 3.85 3.9 4.01
## 3 4 3 5 4 1 4 3 1 1 2 1 2 2The pH levels of wine range from 2.74 to 4.01. Most have values between 3.21 and 3.4. There are multiple outliers in this distribution where the wines have pH levels that are either higher than 3.685 or lower than 2.925.
## 75%
## 1## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.3300 0.5500 0.6200 0.6581 0.7300 2.0000## sulphates
## 0.33 0.37 0.39 0.4 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52
## 1 2 6 4 5 8 16 12 18 19 29 31 27 26 47
## 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67
## 51 68 50 60 55 68 51 69 45 61 48 46 41 42 36
## 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.82
## 35 23 33 26 28 26 26 20 25 26 23 18 19 15 22
## 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97
## 15 13 14 13 13 7 7 8 8 5 10 4 2 3 6
## 0.98 0.99 1 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.1 1.11 1.12
## 2 3 1 1 3 2 2 3 4 2 3 1 2 1 1
## 1.13 1.14 1.15 1.16 1.17 1.18 1.2 1.22 1.26 1.28 1.31 1.33 1.34 1.36 1.56
## 2 2 1 1 5 3 1 1 1 2 1 1 1 3 1
## 1.59 1.61 1.62 1.95 1.98 2
## 1 1 1 2 1 1Sulphate levels range from 0.33 to 2.00. Most values lie between 0.55 and 0.73. There is a right skew in the distribution of sulphate levels. There are multiple outliers in this distribution where the wines have sulphate levels that are higher than 1.
## 75%
## 13.5
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.40 9.50 10.20 10.42 11.10 14.90Most wines have alcohol levels between 9.5 and 11.1. The minimum is 8.4 and the maximum value is 14.9. There is a right skew in the distribution of alcohol levels. There are multiple outliers in this distribution where the wines have alcohol levels that are higher than 13.5.
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.000 5.000 6.000 5.636 6.000 8.000## quality
## 3 4 5 6 7 8
## 10 53 681 638 199 18The quality ratings of wine range from 3 to 8. Most wines having a rating of 5 or 6.
The dataset contains 1599 types of wines each with 11 independent variables that are based on physicochemical tests and one dependent variable. The dependent variable is the measurement of quality which is based on sensory data provided by wine experts.
The univariate analysis of the red wine dataset revealed interesting distributions in alcohol, fixed acidity, and sulphates. Each of these variables has long tails which I will investigate further in my bi-variate analysis. I suspect that these variables have an influence on the quality of the wine.
The other two variables that I will examine in more detail are citric acid and total sulfur dioxide. Citric acid is added to finished wines to increase acidity and give the wine a ‘fresh flavor.’ If too much is added, it can increase the formation of volatile acid which gives wines a vinegar taste. There may be a ‘sweet spot’ for this variable which I will explore in more detail. Plotting the values of total sulfur dioxide revealed a bi modal distribution which may be related to the quality of the wine.
I added an additional variable called ‘binary.quality’ that will divide the wines into two categories- good or bad. Wines that have a quality rating of 6 or higher are deemed good. Any wine with a rating less than 6 is considered bad. Creating these two groups will help to uncover patterns from a bi-variate and multivariate analysis.
A pair-plot of the variables in the dataset reveals that alcohol, volatile acidity, and citric acid seem to have a strong relationship with the quality of a wine. I will explore these relationships further.
## wine$binary.quality: Bad
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.1800 0.4600 0.5900 0.5895 0.6800 1.5800
## --------------------------------------------------------
## wine$binary.quality: Good
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.1200 0.3500 0.4600 0.4741 0.5800 1.0400
The boxplot above shows that the variance for volatile acidity in good and bad wines is similar. Bad wines have a higher mean and median. The mean and median volatile acidity for good wines was 0.4741 and 0.46 respectively. The mean and median volatile acidity for bad wines was 0.5895 and 0.59 respectively. A frequency polygon of volatile acidity by wine quality shows that the higher the volatile acidity, the more likely a wine is to be of bad quality. Most wines above a volatile acidity of 0.6 were of bad quality.
## wine$binary.quality: Bad
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.3300 0.5200 0.5800 0.6185 0.6500 2.0000
## --------------------------------------------------------
## wine$binary.quality: Good
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.3900 0.5900 0.6600 0.6926 0.7700 1.9500
Sulphate levels also vary between wines of different qualities. Good quality wines had higher mean and median sulphate levels. The mean and median values for good wines were 0.6926 and 0.66 respectively. Wines of poor quality had mean and median sulphate levels of 0.6185 and 0.58 respectively. A frequency polygon of sulphate levels by wine quality reveals that those with higher levels have a greater likelihood of being good wines. Wines that had sulphate levels of 0.63 or higher tend to be of good quality.
## wine$binary.quality: Bad
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.400 9.400 9.700 9.926 10.300 14.900
## --------------------------------------------------------
## wine$binary.quality: Good
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.40 10.00 10.80 10.86 11.70 14.00
Alcohol content varies depending on the quality of the wine. Wines of good quality have a higher variance as well as a higher mean and median. The mean and median alcohol content for good wines was 10.86 and 10.8 respectively. Bad wines had a mean alcohol content of 9.926 and a median of 9.7. A frequency polygon of alcohol content by wine quality shows that wines with alcohol levels above 10.25 have a higher likelihood of being of good quality.
## wine$binary.quality: Bad
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 6.00 23.75 45.00 54.65 78.00 155.00
## --------------------------------------------------------
## wine$binary.quality: Good
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 6.00 20.00 33.00 39.35 50.00 289.00
Wines of poor quality have a larger variance in total sulfur dioxide levels as well as a higher mean and median. Wines of bad quality have a median of 45 and a mean of 54.65. Wines of good quality have a mean of 39.35 and a median of 33. A plot of the frequency of total sulfur dioxide levels by wine quality suggests that wines with levels above 80 are more likely to be of bad quality.
## wine$binary.quality: Bad
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.0800 0.2200 0.2378 0.3600 1.0000
## --------------------------------------------------------
## wine$binary.quality: Good
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.1150 0.3100 0.2999 0.4600 0.7800
A box plot of the citric acid content of wines by quality reveals that good wines have a higher median and variance than bad wines. Good wines also have a higher mean citric acid. The mean and median levels for good wines are 0.46 and 0.31 respectively. Bad wines have a mean of 0.2378 and a median of 0.22. Plotting the frequency of citric acid levels by wine quality suggests that good wines have higher citric acid levels. One notable aspect of this data is that it does not show that at high levels, citric acid can affect the quality of the wine. Citric acid can increase the formation of volatile acid. One would expect that there would be a resurgence of bad wines at higher levels.
## [1] -0.06166827A bi-variate analysis of the dataset reveals that good wines have tend to have a higher alcohol content as well as lower levels of volatile acidity. These two variables do not seem to have a significant correlation with each other, but I will explore this relationship in more detail in my multivariate analysis.
One interesting relationship that wasn’t a main feature of interest, is that of fixed acidity and density. These two variables seem to have a significant correlation. This will be explored further.
## [1] -0.6829782Fixed acidity and pH have the strongest correlation among all the variables analyzed in this dataset. The correlation coefficient for these two variables is -0.6829782. This would make sense because the pH scale is a measure of how basic or acidic a substance is. One would expect a high correlation for these two variables.
## [1] 0.6680473In the previous section, I noted that density and fixed acidity seem to have a significant correlation. I examined this relationship further by creating a scatter plot of the two variables and labeling each point based on the quality of the underlying wine. It seems like at lower fixed acidity levels, good wines tend to have lower densities.
It seems like the higher the alcohol content and lower the volatile acidity of a wine, the more likely it is to be of good quality.
Higher sulphate levels and alcohol content also seem to be indicators of a good wine.
Similarly, wines with higher alcohol and citric acid levels tend to be of good quality.
Wines with higher alcohol, volatile acidity, and sulphate levels tend to be of better quality. One could use these features to construct a linear model to predict the quality of a red wine.
##
## Calls:
## m1: lm(formula = I(quality ~ alcohol), data = wine)
## m2: lm(formula = quality ~ alcohol + volatile.acidity, data = wine)
## m3: lm(formula = quality ~ alcohol + volatile.acidity + sulphates,
## data = wine)
##
## =====================================================
## m1 m2 m3
## -----------------------------------------------------
## (Intercept) 1.875*** 3.095*** 2.611***
## (0.175) (0.184) (0.196)
## alcohol 0.361*** 0.314*** 0.309***
## (0.017) (0.016) (0.016)
## volatile.acidity -1.384*** -1.221***
## (0.095) (0.097)
## sulphates 0.679***
## (0.101)
## -----------------------------------------------------
## R-squared 0.2 0.3 0.3
## adj. R-squared 0.2 0.3 0.3
## sigma 0.7 0.7 0.7
## F 468.3 370.4 268.9
## p 0.0 0.0 0.0
## Log-likelihood -1721.1 -1621.8 -1599.4
## Deviance 805.9 711.8 692.1
## AIC 3448.1 3251.6 3208.8
## BIC 3464.2 3273.1 3235.7
## N 1599 1599 1599
## =====================================================Example red wine:
Alcohol: 13, Volatile Acidity: 0.32, Sulphates: 0.85, Quality: 7
## fit lwr upr
## 1 6.816987 5.521736 8.112239It appears that a model that includes alcohol, volatile acidity, and sulphates can be used to predict the quality of a wine. The wine that was used to test this model had a quality rating of 7. The model predicted a rating of 6.816987. One limitation of this model is that since it uses linear regression, it is sensitive to outliers. For example, there may be cases were a good wine may have a relatively low alcohol conent, which would affect the accuracy of this model.
Most wines with a volatile acidity less than 0.6 tend to be of good quality. Wines with a volatile acidity higher than 0.6 were more likely to be of bad quality.
Most wines with an alcohol content greater than 10% are of good quality. There are significantly more wines with alcohol contents between 9 and 10% that are of bad quality.
Wines with higher alcohol contents and lower volatile acidity levels were more likely to be of good quality. Most wines with alcohol contents greater than 10% and volatile acidity levels lower than 0.6 (g / dm^3) are of good quality.
Exploring the wine dataset revealed a relationship between the volatile acidity, alcohol content, and quality of a wine. A univariate analysis of these variables revealed skewed distributions, which seem to be a function of the underlying quality of the wines. Prior to conducting a bi-variate and multivariate analysis, the wines were divide into two groups(good/bad). Encoding the wines with a binary variable helped to discern which features had the most influence over the quality of wines. The higher the alcohol content of a wine, the more likely it is of good quality. Good quality wines also have lower volatile acidity levels. A mulivariate analysis of these features suggested that the quality of a wine could be predicted based on volatile acidity and alcohol levels. A linear regression model was constructed to predict the quality of a wine based off its alcohol content, sulphates, and volatile acidity.Further work may be done to assess the accuracy of this model. A larger dataset may reveal other findings that were not included in this study.
P. Cortez, A. Cerdeira, F. Almeida, T. Matos and J. Reis. Modeling wine preferences by data mining from physicochemical properties. In Decision Support Systems, Elsevier, 47(4):547-553. ISSN: 0167-9236.